If
[tex]S=1+2+\cdots+(n-1)+n[/tex]
then it's also true that
[tex]S=n+(n-1)+\cdots+2+1[/tex]
so that
[tex]2S=(1+n)+(2+(n-1))+\cdots+((n-1)+2)+(n+1)=n(n+1)\implies S=\dfrac{n(n+1)}2[/tex]
For any integer [tex]n[/tex], [tex]n(n+1)[/tex] is even. We have [tex]5\mid S[/tex] if either [tex]5\mid n[/tex] or [tex]5\mid(n+1)[/tex]. This means [tex]n[/tex] must satisfy either [tex]n\equiv0\pmod5[/tex] or [tex]n\equiv4\pmod5[/tex], in which case we have a general solution of
[tex]n=5k[/tex]
or
[tex]n=5k-1[/tex]
where [tex]k[/tex] is any integer.
the sum of the real numbers x and y is 25. their difference is 13. what is the value of xy?
The sum of the real numbers x and y is 25 and their difference is 13. To find the value of xy, we need to solve a system of equations. The value of xy is 114.
Explanation:To solve this problem, we need to set up a system of equations based on the given information. Let's denote x and y as the two real numbers. The sum of x and y is 25, so we can write the equation x + y = 25. The difference between x and y is 13, so the equation becomes x - y = 13. To find the value of xy, we need to solve this system of equations.
First, let's add the two equations together. (x + y) + (x - y) = 25 + 13. This simplifies to 2x = 38. Dividing both sides by 2, we find x = 19.
Now, we can substitute the value of x into one of the original equations (x + y = 25) to solve for y. 19 + y = 25. Subtracting 19 from both sides, we get y = 6.
Therefore, the value of xy is 19 * 6 = 114.
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Simplify 4x2(2x2− 8x + 6). (1 point) 8x2− 32x + 24 6x2− 32x + 24 6 − 32x + 24x2 8x4− 32x3+ 24x2
the asnwer is most likey 12x^4-32x^3+24x^2
Answer:
Last option: [tex]8x^4-32x^3+24x^2[/tex]
Step-by-step explanation:
Given the expression [tex]4x^2(2x^2-8x + 6)[/tex], you need to remember the Product of powers property, which states the following:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Knowing this, you can apply the Distributive property. Therefore, you get:
[tex](4x^2)(2x^2)-(8x)(4x^2) +(6)(4x^2)=8x^{(2+2)}-32x^{(1+2)}+24x^2=8x^4-32x^3+24x^2[/tex]
You can observe that this matches with the las option.
What is the slope of the line whose equation is 2x - 4y = 10?
Please I need this right away !
Answer:
1/2
or
0.5
Step-by-step explanation:
you need to get the line in the form of y = mx + b
2x - 4y = 10 Subtract 3x from both sides
-4y = - 2x + 10 3x on the left disappears. Divide by - 4
-4y/-4 =-2x/-4 +10/-4 Do the division
y = (2/4)x - 2.5
y = (1/2)x - 2.5
The slope is the number in front of the x
y = 0.5x - 2.5
A carnival game has the possibility of scoring 50 points, 75 points, or 150 points per turn. The probability of scoring 50 points is 60%, 75 points is 30%, and 150 points is 10%. The game operator designed a simulation using a random number generator to predict how many points would be earned for a turn.
Integer Value Points Frequency
0 - 5 50 55
6 - 8 75 32
9 150 13
10. What is game’s expected value of points earned for a turn?
(SHOW WORK)
Answer:
The game’s expected value of points earned for a turn is 71.
Step-by-step explanation:
Here we know that:
Points Frequency
50 55
75 32
150 13
Here points earned is a random variable.
We need to find its expected value,
Finding Expected value:
Expected value of a random variable is its mean value. So we will first find the mean value of points earned per turn from the table we are given.
Total number of turns = sum of frequencies
= 55 + 32 + 14 = 100
Total points earned = 50(55) + 75(32) + 150(13)
= 7100
Expected value of points earned for a turn = Mean value of points
= Total points/no. of turns
= 7100/100
= 71
The _____ a0 of a segment divides the segment into two segments of equal length.
The Midpoint of a segment divides the segment into two segments of equal length.
Answer:
Midpoint
Step-by-step explanation:
The midpoint is the point on the segment halfway between the two endpoints. In some cases the midpoint of a segment can be found simply by counting.
For example in a straight line between (2,0) and (6,0) the midpoint would be located on the point (4,0).
Can someone please help me with this question asap! greatly appreciated!
Answer:
1344 ft^2
Step-by-step explanation:
From the picture we can see that 4w = 3l, which means that l = (4/3)w. Since w = 12 ft, l = (4/3)(12 ft) = 16 ft. Then the total area of the floor is
(length of floor)(width of floor) = (48 ft)(12 ft + 16 ft) = 1344 ft^2
Using these integers 12345789 you put them in 2 groups of 4 coming up with the same summ
What is the surface area of the figure?
Answer:
The surface area of the figure is [tex]SA=458\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the figure is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the L-shaped cross section
P is the perimeter of L-shaped cross section
H is the width of the figure
Find the area of the L-shaped cross section
[tex]B=12*7+5*5=109\ ft^{2}[/tex]
Find the perimeter P of L-shaped cross section
[tex]P=(12+7+7+5+5+12)=48\ ft[/tex]
[tex]H=5\ ft[/tex]
substitute
[tex]SA=2(109)+(48)(5)=458\ ft^{2}[/tex]
Answer:
Surface area = 458 square ft
Step-by-step explanation:
From the figure attached with this answer we can see figure.
To find the surface area of the figure
Surface area is sum of area of small rectangles
Surface area = 2(12 * 7 ) + 4(5 * 5) + 2(12 * 5) + 2(7 * 5)
= 2*84 + 4*25 + 2 *60 + 2*35
= 168 + 100 + 120 + 70
= 458
Therefore surface area of given figure = 458 square ft
What is the reflection image of (5,-3) across the line y = -x?
Simplify (5√2-1)^2
10 √2+51
-10 √2+51
41 √2
What is the solution to the linear equation?
4b + 6 = 2 – b + 4
Answer:
[tex]\large\boxed{b=0}[/tex]
Step-by-step explanation:
[tex]4b+6=2-b+4\qquad\text{combine like terms}\\\\4b+6=(2+4)-b\qquad\text{add}\ b\ \text{to both sides}\\\\5b+6=6\qquad\text{subtract 6 from both sides}\\\\5b=0\qquad\text{divide both sides by 5}\\\\b=0[/tex]
Hello!
Answer:
[tex]\boxed{b=0}\checkmark[/tex]
The answer should have a positive sign.
Step-by-step explanation:
First, switch sides and group like terms.
4b+6=-b+2+4
Then, add numbers from left/right.
2+4=6
4b+6=-b+6
Subtract by 6 both sides of an equation.
4b+6-6=-b+6-6
Simplify.
4b=-b
Next add b both sides of an equation.
4b+b=-b+b
Simplify.
5b=0
Therefore, you divide by 5 from both sides of an equation.
5b/5=0/5
Finally, you simplify and solve to find that answer is.
0/5=0
b=0 is the correct answer.
Hope this helps!
Have a nice day! :)
-Charlie
Thank you so much!
What is the area of the hexagon?
(See image attached below)
Answer:
57.12cm²
Step-by-step explanation:
From the attached picture, you will notice that you can fill in the 4 corners of the hexagon with 4 triangles (i.e shaded areas) to form a rectangle.
Area of each shaded corner (triangle) = [tex]\frac{1}{2}[/tex] x 4 x 2.14 = 4.28 cm²
Area of 4 shaded corners = 4 x 4.28 = 17.12cm²
Area of rectangle = 9.28 x 8 = 74.24 cm²
Area of hexagon
= Area of rectangle - Area of 4 shaded corners
= 74.24 - 17.12
= 57.12cm²
Which scenario could be represented by the algebraic expression n/12?
Answer:
Step-by-step explanation:
A pie weighs n pounds. How much would one serving weigh if the entire pie were to be shared equally among 12 people?
A sphere has a diameter of 12 ft. What is the surface area of the sphere? Express the answer in terms of pi.
Recall the formula SA=4 pi r^2.
pi ft^2
Answer:
[tex]SA=144\pi\ ft^2[/tex]
Step-by-step explanation:
We know that the diameter of the sphere is 12 feet.
By definition the radius of the sphere is:
[tex]r =\frac{d}{2}[/tex]
Where d is the diameter of the sphere
Then
[tex]r =\frac{12}{2}[/tex]
[tex]r =6\ ft[/tex]
Now we calculate the surface area of the sphere using the formula
[tex]SA=4\pi r^2[/tex]
[tex]SA=4\pi (6)^2[/tex]
[tex]SA=4\pi(36)[/tex]
[tex]SA=144\pi\ ft^2[/tex]
The coordinates of points A and B (2, 3) and (-2,-4) respectively.what is the slope of the line that connects two points
Answer:
7/4
Step-by-step explanation:
The slope of the line going through (2,3) and (-2,-4) can be found by:
A) Lining up points
B) Subtracting the numbers vertically
C) Answer: Putting 2nd difference over 1st difference (yes a fraction)
Let's do it!
( 2 , 3)
-( -2 , -4)
--------------
4 7
So the slope is 7/4
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y2-y1} {x2-x1}[/tex]
We have as data the following points:
[tex](x1, y1) = (2,3)\\(x2, y2) = (- 2, -4)[/tex]
Substituting in the formula we have:
[tex]m = \frac {-4-3} {- 2-2}[/tex]
Equal signs are added and the same sign is placed:
[tex]m = \frac {-7} {- 4}\\m = \frac {7} {4}[/tex]
Answer:
[tex]m = \frac {7} {4}[/tex]
Write an expression to represent the perimeter of 12a, 6a+8, 10a-4, 6a+8
Answer:
34a + 12
Step-by-step explanation:
12a + 6a + 8 + 10a - 4 + 6a + 8
combine like terms
12a + 6a + 10a + 6a
and 8 + 8 - 4
34a + 12
Rhea is solving a math puzzle. To find the solution of the puzzle, she must find the product of two numbers. The first number is the sum of 23 and x, and the second number is 18 less than two times the first number. Which of the following functions represents the product of these two numbers?
Opions are:
A.
P(x) = 2x^2 + 74x + 644
B.
P(x) = 2x^2 + 28x - 414
C.
P(x) = 2x^2 + 102x + 1,288
D.
P(x) = 2x^2 + 110x + 1,472
Answer:
It's B.
Step-by-step explanation:
First is x + 23 and second is 2x - 18.
So the product is
(x + 23)(2x - 18)
= 2x^2 - 18x + 46x - 414
= 2x^2 + 28x - 414
There are three kids. The sum of individual squares of their body weights (2 + 2 + 2) is 100. The sum of the product of their weights taking two friends at a time i.e. + + is 150. What will the weighing machine read if all the three kids stand on it at the same time?
Answer:
20
Step-by-step explanation:
Givens
Let child one = x
Let child two = y
Let child three = z
Equations
x^2 + y^2 + z^2 = 100
xy + xz + yz = 150
Solution
There's a trick here. The square of their weights added together is equal (with some modification) to the given conditions. Start by squaring (x+y+z).
(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz
Take out 2 as a common factor from the last three terms.
(x + y + z)^2 = (x^2 + y^2 + z^2+ 2(xy + xz + yz) )
Substitute the given conditions into the equation. (x^2 + y^2 + z^2) = 100 and 2*(xy + xz + yz) = 2 * 150
(x + y + z)^2 = 100 + 2*150
(x + y + z)^2 = 100 + 300
(x + y + z)^2 = 400
Take the square root of both sides.
sqrt(x+y+z)^2 = sqrt(400)
x + y + z = 20
Note
This answer tells you nothing about the values of x y and z. On the other hand it does not ask for the values of x y and z.
4+ 2 sin x=14-8 sin x for 0° < x < 180°
Answer:
x = 90° or π/2 rad
Step-by-step explanation:
4+ 2 sin x=14-8 sin x
2 sin x + 8 sin x = 14 - 4
10 sin x = 10
sin x = 1
Using a calculator
x = sin[tex]sin^{-1}[/tex]1
x = 90° or π/2 rad
x = 90° or π/2 rad
What is the best way to learn trigonometry?
If you are in high school, take Algebra one or two, Trigonometry, Analytic Geometry, or Precalculus. If you're in college take College Algebra, Trig, or then Calculus.
‘IT IS HARD.’ WHY IS TRIGONOMETRY IMPORTANT?It really is not hard.The reason why trigonometry is very important lies all around us everyday, although most of us are blissfully unaware.Navigation or surveying are also heavily dependent on trigonometry.So, the is trigonometry important.4+ 2 sin x=14-8 sin x
2 sin x + 8 sin x = 14 - 4
10 sin x = 10
sin x = 1
Using a calculator
x = sin1
x = 90° or π/2 rad
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Theo has $5 more than denise and denise has $11 more than rudy . Together , they have $45. How much money does denise have?
Answer:
Denise has $17
Step-by-step explanation:
T = Theo, D = Denise, and R = Rudy
T + D + R= 45
(D+ 5) +( D)+ (D - 11) = 45
3D -6 = 45
3D = 51
D = 17
solve this problem in order of operations 4-[6(3x+2)-x]+4
[tex]4-(6(3x+2)-x)+4=-(18x+12-x)+8=-(17x+12)+8=-17x-12+8=-17x-4[/tex]
If the alternate hypothesis of an experiment is “The true mean height of the giraffes is more than 15 feet” what is the null hypothesis?
Answer: "The true mean height of the giraffes is less than or equal to 15 feet".
Step-by-step explanation:
A hypothesis in a statement that is made about a statistical parameter of a population.
A null hypothesis [tex]H_0[/tex] is usually the hypothesis that is tried to reject by an alternate hypothesis [tex]H_a[/tex]
In this case [tex]H_a[/tex] is:
"The true mean height of the giraffes is more than 15 feet".
Therefore, for this case, the null hypothesis must be:
"The true mean height of the giraffes is less than or equal to 15 feet".
What is the period of f(x)=sin(x)?
-Pi/2
-Pi.
-3pi/2.
-2pi
Answer:
2pi
Step-by-step explanation:
period for sin is 2pi/b
its only x theres 1 before x so its 1x=b
2pi/1
= 2pi
The period of function f ( x ) = sin ( x ) is 2π.
The sine function ( sin ( x ) ) is a periodic function, which means it repeats its values in regular intervals. The period of sin(x) is the length of one complete cycle of the function before it starts repeating itself.
The period of the function f ( x ) = sin( x ) is 2π.
In the case of sin ( x ), it completes one full cycle ( from 0 to 2π ) every 2π units. Therefore, the period of f ( x ) = sin ( x ) is 2π.
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Find the perimeter of the following shapes.
Answer:
4. (a) = 12 m
(b) = 27 cm
(c) = 24 mm
(d) = 18 km
(e) = 10 m
(f) = 36 cm
Step-by-step explanation:
Perimeter is sum the distance round a figure.
if a shape has those, they signify that the shape has two side that are equal
a) 4 + 4 + 2 + 2 = 12. The top part is equal to the bottom part signified by those two lines. And the left is equal to the right .
b) 10 + 10 + 7 = 27
c) 5 + 5 + 8 + 6 = 24
d) 3 + 3 + 6 + 6 = 18
e) 2.5 + 2.5 + 2.5 + 2.5 = 10
f) 12 + 7 + 7 + 5 + 5 = 36
If you need any clarification or more explanation pls do mention in the comment section. i would like to help more.
Hope this helps and if it does pls mark as branliest answer thx.
Please help.. will mark Brainliest!
Answer:
128 degrees, so C is again the answer.
Step-by-step explanation:
Since angles 3 and 11 are corresponding(from your previous question), angles 1 and 11 will add up to 180 degrees, since a line is that long. Therefore your answer is 180-(degrees of angle 1)= 180-52= 128
m∠11 = 128°.
A line that cuts three parallel lines forms congruent angles which means they measure the same.
In this problem m∠1 = 52° = m∠4 = m∠5 = m∠8 = m∠9 = m∠12, and m∠2 = m∠3 = m∠6 = m∠7 = m∠10 = m∠11.
To calculate m∠11, we know that m∠12 = m∠1 = 52°, the sum of the angle of m∠11 and m∠12 is 180°. Then:
m∠11 + m∠12 = 180°, with m∠1 = 52° = m∠12
m∠11 + 52° = 180°
m∠11 = 180° - 52°
m∠11 = 128°
The presence of an angle bisector will result in what type of angles ?
Answer:
Congruent Angles
Reasoning:
An angle bisector bisects/splits an angle into two equal/congruent parts/angles.
Answer with explanation:
→ The Meaning of Angle bisector is that line or line segment which divide an Angle in two equal Parts.
→So, If a Line or line segment that is Angle bisector is bisecting an Angle , it will divide the angle into two equal Angles.
For example: Suppose an Angle has Measure of 60°, the Angle bisector will divide it into two congruent Angles each being equal to 30°.
⇒The presence of an angle bisector will result in Congruent type of angles
Enter the correct value so that each expression is a perfect-square trinomial.
x2 – 10x +
Answer:
[tex]x^2-10x+25[/tex]
Step-by-step explanation:
We have been given an expression [tex]x^2-10x+[/tex]. We are asked to convert our given expression into perfect-square trinomial.
We know that an equation in form [tex]x^2+bx+c[/tex] is a perfect square, if [tex]c=(\frac{b}{2})^2[/tex]
To convert our given expression into perfect-square trinomial, we need to add [tex](\frac{10}{2})^2[/tex] to our given expression.
[tex](\frac{10}{2})^2=5^2=25[/tex]
Therefore, our perfect square trianominal would be [tex]x^2-10x+25[/tex].
Question 1 of 10
2 Points
The slope of the line below is – 3. Use the coordinates of the labeled point to
find a point-slope equation of the line.
(5.-7)
Answer:
[tex]\large\boxed{y+7=-3(x-5)}[/tex]
Step-by-step explanation:
[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_2)-point\\\\\text{We have}\ m=-3\ \text{and}\ (5,\ -7).\\\text{Substitute:}\\\\y-(-7)=-3(x-5)\\y+7=-3(x-5)[/tex]
Which of the following pair(s) of circles have /as a common internal tangent? Select all that apply.
A and B
A and C
B and C
Answer:
A and B, A and C
Step-by-step explanation:
A and B touch at T same as A and C. The tangent is in between the two circles but through the touching points. B and C share the tangent but externally since at T it does not pass in between them.
Consider the graph of the equation y = 5. Which statements are true? Check all that apply.
The graph of y = 5 is a vertical line.
The graph of y = 5 is a horizontal line.
The graph of y = 5 is neither a vertical line nor a horizontal line,
The point (5,3) lies on the line.
The point (-4, 5) lies on the line.
Answer:
y=5 is horizontal
(-4,5) is on the line
Step-by-step explanation:
y= a number is always a horizontal line
x= b number is always a vertical line
So y=5 is horizontal and it includes every single ordered pair with a y-coordinate of 5. So it contain the ordered pair (-4,5).
So there are two statements.
The correct statements are :
The graph of y = 5 is a vertical line.
The point (-4, 5) lies on the line.
What are equations?An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.
How to know which statements are true?The equation y = 5 is a line parallel to the y axis .So, the line is vertical.The line also passes through all the points with ordinate 5
So the line passes through ( -4,5)
So options A and D are correct.
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